According to Mail Online, the Gas have their radar on the Blues left-back.
Haunstrup has made 19 appearances for Kenny Jackett’s side this season, including five in a makeshift right-back role.
He was sidelined for more than a month with a knee problem he sustained against Peterborough on December 7.
Since returning to full fitness, the academy graduate has found himself behind Brimingham loanee Steve Seddon in the pecking order.
Haunstrup’s current two-year deal expires at the end of the campaign, with contract negotiations still to be opened up.
The Waterlooville lad’s situation has apparently alerted Rovers, with Mail Online claiming they're ‘keen to strike a deal’ before the transfer window shuts on Friday.
But Gallen says Pompey have had no contact from their League One rivals.
The assistant boss said: ‘I have not heard anything. I probably would have done but I've not heard anything.
‘It was mentioned to me (the rumour) earlier today but I’ve not heard anything.
‘Not only has Brandon played left-back, but he had a decent spell at right-back at a time when we also won games.
‘He’s done pretty well there and Brandon can play both positions.
‘Steve has got the shirt and he’s not going to relinquish it very easily.’
In total, Haunstrup has made 56 appearances for Pompey, scoring one goal.